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<br> <h1> Link to the source code for this example: </h1>
<a href="https://github.com/libMesh/libmesh/tree/master/examples/vector_fe/vector_fe_ex3" target="_blank">Open vector_fe_ex3 in new tab.</a>
<a name="output"></a>
<br><br><br> <h1> The console output of the program: </h1>
<pre>
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt element_type=TRI6 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=800
    n_local_elem()=800
    n_active_elem()=800
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=1240
    n_local_dofs()=1240
    max(n_local_dofs())=1240
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1240
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 4.87097
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 5
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 23.6078
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 1.0869e-13
Trying full Newton step
  Current Residual: 1.5625e-13
  Nonlinear solver converged, step 0, residual reduction 6.61855e-15 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.128366
HCurl semi-norm error is: 0.655952
HCurl-Error is: 0.668394

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt element_type=TRI6 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt element_type=TRI7 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=2481
    n_local_nodes()=2481
  n_elem()=800
    n_local_elem()=800
    n_active_elem()=800
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=1240
    n_local_dofs()=1240
    max(n_local_dofs())=1240
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=1240
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 4.87097
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 5
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 23.6078
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 1.07153e-13
Trying full Newton step
  Current Residual: 1.57019e-13
  Nonlinear solver converged, step 0, residual reduction 6.65114e-15 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.128366
HCurl semi-norm error is: 0.655952
HCurl-Error is: 0.668394

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt element_type=TRI7 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt element_type=QUAD8 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1281
    n_local_nodes()=1281
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=840
    n_local_dofs()=840
    max(n_local_dofs())=840
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=840
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 6.71429
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 7
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 28.9779
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 3.95978e-14
Trying full Newton step
  Current Residual: 7.02729e-14
  Nonlinear solver converged, step 0, residual reduction 2.42505e-15 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.12862
HCurl semi-norm error is: 0.802879
HCurl-Error is: 0.813116

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt element_type=QUAD8 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt element_type=QUAD9 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="FIRST"
    n_dofs()=840
    n_local_dofs()=840
    max(n_local_dofs())=840
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=840
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 6.71429
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 7
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 28.9779
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 3.99601e-14
Trying full Newton step
  Current Residual: 7.14395e-14
  Nonlinear solver converged, step 0, residual reduction 2.46531e-15 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.12862
HCurl semi-norm error is: 0.802879
HCurl-Error is: 0.813116

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt element_type=QUAD9 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=TRI6 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=800
    n_local_elem()=800
    n_active_elem()=800
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="SECOND"
    n_dofs()=4080
    n_local_dofs()=4080
    max(n_local_dofs())=4080
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=4080
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 11.4118
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 14
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 47.591
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 7.29357e-13
Trying full Newton step
  Current Residual: 1.77284e-12
  Nonlinear solver converged, step 0, residual reduction 3.72517e-14 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.00575821
HCurl semi-norm error is: 0.0398913
HCurl-Error is: 0.0403047

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=TRI6 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=TRI7 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=2481
    n_local_nodes()=2481
  n_elem()=800
    n_local_elem()=800
    n_active_elem()=800
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="SECOND"
    n_dofs()=4080
    n_local_dofs()=4080
    max(n_local_dofs())=4080
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=4080
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 11.4118
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 14
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 47.591
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 6.88575e-13
Trying full Newton step
  Current Residual: 1.77577e-12
  Nonlinear solver converged, step 0, residual reduction 3.73131e-14 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.00575821
HCurl semi-norm error is: 0.0398913
HCurl-Error is: 0.0403047

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=TRI7 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=QUAD8 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1281
    n_local_nodes()=1281
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="SECOND"
    n_dofs()=3280
    n_local_dofs()=3280
    max(n_local_dofs())=3280
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3280
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 16.6341
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 22
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 20.864
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 6.17245e-13
Trying full Newton step
  Current Residual: 1.26787e-12
  Nonlinear solver converged, step 0, residual reduction 6.07684e-14 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.00520051
HCurl semi-norm error is: 0.0326373
HCurl-Error is: 0.0330491

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=QUAD8 -pc_type lu
***************************************************************
***************************************************************
* Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=QUAD9 -pc_type lu
***************************************************************

 Mesh Information:
  elem_dimensions()={2}
  spatial_dimension()=2
  n_nodes()=1681
    n_local_nodes()=1681
  n_elem()=400
    n_local_elem()=400
    n_active_elem()=400
  n_subdomains()=1
  n_elemsets()=0
  n_partitions()=1
  n_processors()=1
  n_threads()=1
  processor_id()=0
  is_prepared()=true
  is_replicated()=true

 EquationSystems
  n_systems()=1
   System #0, "CurlCurl"
    Type "Implicit"
    Variables="u"
    Finite Element Types="NEDELEC_ONE"
    Approximation Orders="SECOND"
    n_dofs()=3280
    n_local_dofs()=3280
    max(n_local_dofs())=3280
    n_constrained_dofs()=0
    n_local_constrained_dofs()=0
    max(local unconstrained dofs)=3280
    n_vectors()=1
    n_matrices()=1
    DofMap Sparsity
      Average  On-Processor Bandwidth <= 16.6341
      Average Off-Processor Bandwidth <= 0
      Maximum  On-Processor Bandwidth <= 22
      Maximum Off-Processor Bandwidth <= 0
    DofMap Constraints
      Number of DoF Constraints = 0

Assembling the System
Nonlinear Residual: 20.864
Linear solve starting, tolerance 1e-12
Linear solve finished, step 1, residual 6.17982e-13
Trying full Newton step
  Current Residual: 1.30813e-12
  Nonlinear solver converged, step 0, residual reduction 6.2698e-14 < 1e-06
  Nonlinear solver relative step size inf > 1e-06
L2-Error is: 0.00520051
HCurl semi-norm error is: 0.0326373
HCurl-Error is: 0.0330491

***************************************************************
* Done Running Example vector_fe_ex3:
*   ./example-opt order=2 element_type=QUAD9 -pc_type lu
***************************************************************
</pre>
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